Aspergers Syndrome Foundation - Frequently Asked Questions
Some research shows that there are strikingly similar features in first or second degree relatives on either side of the family, or the family history includes "eccentric" individuals who have a mild expression of the syndrome. There are also some families with a history of children with AS and classic Autism. Should a relative have had similar characteristics when younger, they have a unique advantage in helping the child - they know what they are going through. There is no formal identification of the precise means of transmission if the cause is genetic, but we do have some suggestions as to which chromosomes may be involved. As our knowledge of genetics improves, we may soon be able to predict the recurrence rate for individual families.
In general, there seems to be a genetic component to aspergers and autism, but the exact links are unknown. And, there is no way to tell how much of a risk an individual family has at this point. Still, of the people I know who have aspergers themselves who married and have children, the children also have some form of autism.